[Paper Review] Beamforming for Simultaneous Wireless Information and Power Transfer in Two-Way Relay Channels

Wei Wang, Rui Wang+1 more|arXiv (Cornell University)|Apr 14, 2016

Energy Harvesting in Wireless Networks22 references3 citations

TL;DR

This paper proposes a beamforming and power splitting (PS) optimization framework for two-way relay networks with simultaneous wireless information and power transfer (SWIPT), using amplify-and-forward (AF), DF-XOR, and DF-SUP relaying strategies. By decoupling the nonconvex problem into beamforming and PS ratio subproblems, it achieves optimal energy harvesting under QoS and relay power constraints, with numerical results showing significant performance gains through adaptive strategy and weighting selection.

ABSTRACT

This paper studies simultaneous wireless information and power transfer (SWIPT) systems in two-way relaying (TWR) channels. Here, two source nodes receive information and energy simultaneously via power splitting (PS) from the signals sent by a multi-antenna relay node. Our objective is to maximize the weighted sum of the harvested energy at two source nodes subject to quality of service (QoS) constraints and the relay power constraints. Three well-known and practical two-way relay strategies are considered, i.e., amplify-and-forward (AF), bit level XOR based decode-and-forward (DF-XOR) and symbol level superposition coding based DF (DF-SUP). For each relaying strategy, we formulate the joint energy transmit beamforming and PS ratios optimization as a nonconvex quadratically constrained problem. To find a closed-form solution of the formulated problem, we decouple the primal problem into two subproblems. In the first problem, we intend to optimize beamforming vector for a given PS ratio. In the second subproblem, we optimize the PS ratio with a given beamforming vector. It is worth noting that although the corresponding subproblem are nonconvex, the optimal solution of each subproblem can still be found by using certain techniques. We provide numerical results that demonstrate the advantage of adapting the different relaying strategies and weighted factors to harvest energy in two-way relaying channel.

Motivation & Objective

• Address the challenge of energy-constrained source nodes in two-way relay networks by enabling simultaneous information and energy transfer via a multi-antenna relay.
• Design a joint beamforming and power splitting (PS) ratio optimization framework to maximize harvested energy at two source nodes.
• Ensure quality of service (QoS) constraints and relay transmit power limitations are satisfied in the optimization process.
• Investigate three practical relaying strategies—AF, DF-XOR, and DF-SUP—under the SWIPT framework to compare performance trade-offs.
• Develop a decoupled optimization approach to solve the nonconvex problem by separately optimizing beamforming vectors and PS ratios.

Proposed method

• Formulate the joint beamforming and PS ratio optimization as a nonconvex quadratically constrained problem for each relaying strategy (AF, DF-XOR, DF-SUP).
• Decompose the primal problem into two subproblems: optimizing beamforming for a fixed PS ratio, and optimizing PS ratio for a fixed beamforming vector.
• Apply analytical techniques to solve each nonconvex subproblem and derive closed-form solutions for the optimal beamforming vectors and PS ratios.
• Use SINR constraints and power budget constraints to derive expressions for the optimal PS ratio, ensuring $0 < ho^* < 1$.
• Employ equivalent transformations of SINR constraints to express the optimal PS ratio as a minimum of two upper bounds derived from individual user QoS requirements.
• Validate the solution via numerical results comparing performance across different relaying strategies and weighted factors.

Experimental results

Research questions

• RQ1 How can beamforming and power splitting ratios be jointly optimized to maximize energy harvesting in a two-way relay SWIPT system under QoS and power constraints?
• RQ2 What is the performance gain of using different relaying strategies (AF, DF-XOR, DF-SUP) in terms of harvested energy and spectral efficiency?
• RQ3 How does adaptive selection of weighted factors affect the trade-off between energy harvesting and system throughput in SWIPT-enabled two-way relays?
• RQ4 What are the closed-form solutions for beamforming vectors and PS ratios in the nonconvex optimization problem under each relaying strategy?
• RQ5 How do power budget and QoS constraints influence the feasible region and optimal PS ratio in the SWIPT system?

Key findings

• The proposed decoupled optimization approach successfully derives closed-form solutions for beamforming vectors and PS ratios under all three relaying strategies (AF, DF-XOR, DF-SUP).
• The optimal PS ratio is derived as $ ho^* = ext{min}igracevert 1 - rac{ au_1 oldsymbol{ u}_{1,c}^2}{E_2 P_2^* - D_2}, 1 - rac{ au_2 oldsymbol{ u}_{2,c}^2}{G_2 P_1^* - F_2} igracevert $, ensuring both QoS and PS constraints are met.
• Numerical results demonstrate that adapting the relaying strategy and weighted factors significantly improves energy harvesting performance in two-way relay SWIPT systems.
• Optimal beamforming and PS ratio selection under power and QoS constraints yield higher harvested energy compared to fixed or non-adaptive schemes.
• The solution is robust under various channel conditions, with the optimal PS ratio dependent on SINR requirements and relay power allocation.
• Conditions for the existence of a maximum in the objective function are derived, requiring $ a_2 - a_3 > 0 $ and $ a_2 - a_3 < -a_1 $, ensuring a feasible and bounded solution for $ ho^* $.